Mutually exclusive events, fault tree

As an example, in evaluating the safe behavior of 1000 men and women. Table 12.1 shows the percent of the total that either did or did not have occupational injuries. The contributing events (men having injuries and women having injuries) are not mutually exclusive since either or both may have suffered occupational injuries and, subsequently, affected the primary or top event (safe behavior). Hgure 12.7 shows the fault tree for this extremely simple example. By applying the modified formula for non-mutually exclusive events, the probability of an injury event I involving a man M can be calculated as follows ... 

After selecting the MEX command (selection 5) the comma delimited input consists of groups of basic events that are pairwise mutually exclusive. To extend the group to the next and subsequent lines, the first field must be blank. Up to 100 names per group are allowed with a new group starting when a non-blank character is encountered in the first field. The number of pairs that are mutually exclusive is n /[(n-2) 2 ], where n is the number of basic events in the group. An example for the plant blackout fault tree is DG-A-M,DG-B-M,DG-C-M (where means enter). 

Often, in order to speed up and simplify the calculation, the faults and events in a fault tree are sometimes assumed to be mutually exclusive and independent. Under this assumption, probabilities for the OR gates are... 

On the fault tree, when probability rates are known, the analyst simply adds the probability values for the events under an or gate and arrives at the expected probability for the occurrence of the main or top event. However, it is noted that in many systems, events are not mutually exclusive in that more than one can occur at the same time and result in the same outcome. In fact, the OR gate simply indicates that more than one or only one event must occur to affect the main event When there is some probability that more than one event can occur at the same time to affect an outcome, it is known as joint probability. Figure 12.6 shows the overlapping effect, which creates the joint probability theory. The event labeled AB in this diagram indicates that these events would actually be counted twice should formula (12.1) be used by accidentally labeling the event as mutually exclusive. In order to... 

Special Notations There are other logical relationships that can occur in a fault tree. Various notations included with AND and OR symbols indicate the special logical relationships. Some notation systems use other symbols for special logical relationships. For example, two input events for an OR gate may be mutually exclusive. One excludes the other from occurring. An exclusive notation attached to the OR gate indicates this condition. 

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